   Chapter 4.4, Problem 62E

Chapter
Section
Textbook Problem

HOW DO YOU SEE IT? The graph of f is shown in the figure. The shaded region A has an area of 1.5, and ∫ 0 6 f ( x ) d x = 3.5 . Use this information to fill in the blanks.(a) ∫ 0 2 f ( x ) d x =                   (b) ∫ 0 6 f ( x ) d x =                   (c) ∫ 0 6 | f ( x ) | d x =                   (d) ∫ 0 2 − 2 f ( x ) d x =                   (e) ∫ 0 6 [ 2 + f ( x ) ]   d x =                   (f) The average value of f over the interval [0, 6] is                   . (a)

To determine
The blank in the integral represented by, 02f(x)dx=_______

Explanation

Given:

The graph

In the above graph, the shaded region in A, has area 1.5. And the area under complete A+B is 3.5, that is 06f(x)dx=3.5

Explanation:

In the above graph, the shaded area under A depicts where y<0 with area 1.5.

02f(x)dx=1

(b)

To determine
The blank in the integral represented by, 26f(x)dx=_______

(c)

To determine
The blank in the integral represented by, 06|f(x)|dx=_______

(d)

To determine
The blank in the integral represented by, 022f(x)dx=_______

(e)

To determine
The blank in the integral represented by, 06[2+f(x)]dx=_______

(f)

To determine
Theblank in the statement, ‘average value of f over [0,6] is ______.’

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